<p>Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Computing shortest paths is a straightforward task when the network of interest is fully known, and there are a plethora of computational algorithms for this purpose. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions and the Internet at the autonomous system level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks, where numbers of missing links exceed those of observable links. We demonstrate the utility of latent-geometric path finding in problems of cellular pathway reconstruction and communication security.</p>

Livestreaming of child sexual abuse is an established form of online child sexual exploitation
and abuse. However, only a limited body of research has examined this issue. The Covid-19
pandemic has accelerated internet use and user knowledge of livestreaming services
emphasising the importance of understanding this crime. In this scoping review, existing
literature was brought together through an iterative search of eight databases containing peer-
reviewed journal articles, as well as grey literature. Records were eligible for inclusion if the
primary focus was on livestream technology and online child sexual exploitation and abuse,
the child being defined as eighteen years or younger. Fourteen of the 2,218 records were
selected. The data were charted and divided into four categories: victims, offenders,
legislation, and technology. Limited research, differences in terminology, study design, and
population inclusion criteria present a challenge to drawing general conclusions on the
current state of livestreaming of child sexual abuse. The records show that victims are
predominantly female. The average livestream offender was found to be older than the
average online child sexual abuse offender. Therefore, it is unclear whether the findings are
representative of the global population of livestream offenders. Furthermore, there appears to
be a gap in what the records show on platforms and payment services used and current digital
trends. The lack of a legal definition and privacy considerations pose a challenge to
investigation, detection, and prosecution. The available data allow some insights into a
potentially much larger issue.

Approximate Bayesian computing (ABC) and Bayesian Synthetic likelihood (BSL) are two popular families of methods to evaluate the posterior distribution when the likelihood function is not available or tractable. For existing variants of ABC and BSL, the focus is usually first put on the simulation algorithm, and after that the form of the resulting approximate posterior distribution comes as a consequence of the algorithm. In this paper we turn this around and firstly define a reasonable approximate posterior distribution by studying the distributional properties of the expected discrepancy, or more generally an expected evaluation, with respect to generated samples from the model. The resulting approximate posterior distribution will be on a simple and interpretable form compared to ABC and BSL.

Secondly a Markov chain Monte Carlo (MCMC) algorithm is developed to simulate from the resulting approximate posterior distribution. The algorithm was evaluated on a synthetic data example and on the Stepping Stone population genetics model, demonstrating that the proposed scheme has real world applicability. The algorithm demonstrates competitive results with the BSL and sequential Monte Carlo ABC algorithms, but is outperformed by the ABC MCMC.